报 告 人：张雷洪 教授（上海财经大学）
报告题目：A Projected Preconditioned Conjugate Gradient Method for the Linear Response Eigenvalue Problem.
报告时间：2018年1月6日(周六)下午14:30-17:30
报告地点：静远楼204报告厅
报告人简介：
张雷洪，上海财经大学数学学院教授、博导。主要研究方向是最优化理论与计算、数值线性代数、模式识别、数据挖掘等。2008年博士毕业于香港浸会大学数学系，2012年获第四届“应用数值代数奖”，2017年入选上海财经大学百年校庆“百篇优秀论文”。曾赴美国北卡罗来纳州立大学、日本爱知工业大学、美国德克萨斯大学阿灵顿分校等进行访问。已结项国家自然科学青年基金1项，目前主持国家自然科学基金面上项目1项,参与国家重大研究计划1项、国家自然科学基金面上项目1项。现为多个国际知名杂志的编委，至今已发表学术论文20余篇。
报告摘要：
The linear response eigenvalue problem aims at computing a few smallest positive eigenvalues together with the associated eigenvectors of a special Hamiltonian matrix and plays an important role for estimating the excited states of physical systems. A subspace version of the Thouless minimization principle was established by Bai and Li (SIAM J. Matrix Anal. Appl., 33:1075-1100, 2012) which characterizes the desired eigenpairs as its solution. In this talk, we propose a Projected Preconditioned Conjugate Gradient (PPCG lrep) method to solve this subspace version of Thouless’s minimization directly. We show that PPCG lrep is an efficient implementation of the inverse power iteration and can be performed in parallel. It also enjoys several properties including the monotonicity and constraint preservation in the Thouless minimization principle. Convergence of both eigenvalues and eigenvectors are established and numerical experiences on various problems are reported.